The Omega lying confirms the gun was made 1924 or after
1949 would be the Greek letter beta, usually lower case but possibly upper case
Yes, the chambers would be 2 3/4"
'JF' is likely Jean Falla, who made the barrels, often for high end guns
https://www.littlegun.be/arme%20belge/artisans%20identifies%20e%20f/a%20falla%20gb.htm

I would suggest a second opinion regarding the stock. It's a nice gun and repair of the crack will be much easier when small.

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